The sense, to anyone whose knowledge of Latin enables him to recognize that the zodiacal sign Capricorn is a he-goat, is to perform like a goat, especially a kid or young goat; that is, to frolic about in a grotesque manner.
Although the expression “to cut capers” and its meaning were still new in his day, Shakespeare introduces it in Twelfth Night (1601) in a dialog between the two cronies, Sir Toby Belch and Sir Andrew Aguecheek, Act I, scene 3:
Sir Andrew: I am a fellow o’ the strangest mind i’ the world; I delight in masques and revel sometimes altogether.
Sir Toby: Art thou good at these kickshaws, knight?
Sir Andrew: As any man in Illyria, whatsoever he be, under the degree of my betters; and yet I will not compare with an old man.
Sir Toby: What is thy excellence in a galliard (a lively French dance),
Sir Andrew: Faith, I can cut a caper.
Sir Toby: And I can cut the mutton to it.